Thousands of people have rallied around Australia, calling for the government to immediately close its offshore immigration centres following the publication of the Nauru files.

Protests were held in Sydney, Melbourne, Perth, Newcastle, Hobart, Brisbane, Adelaide, Ballina, and at the Australian embassies in London and Tokyo on Saturday. Another rally is planned for Darwin on Sunday, the day after the Northern Territory election.

Chris Breen, a spokesman for the Refugee Action Collective and organiser of the Melbourne rally said about 2,000 people attended.

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“The point was to keep the pressure up on the Turnbull government after the election. We think refugee policy is coming apart at the seams,” Breen told Guardian Australia.

The publication of the Nauru files, which included more than 2,000 incident reports documenting the everyday trauma and distress of detainees on the Pacific island as well as widespread mental illness and frequent acts of violence, showed the ongoing urgency to close the camps and bring the asylum seekers and refugees to Australia, Breen said.

“The abuse isn’t a product of lack of oversight, it’s built into the detention system.”

A former teacher from Nauru addressed the Melbourne crowd and shared her experiences in the centre, including an incident when guards ran a mock serious response scenario, including ambulances and fake blood, but didn’t warn detainees. The exercise was held in front of the school, she said.

Behrouz Bouchani, a Kurdish Iranian journalist currently detained on Manus, said he had witnessed the same “system of abuse” as that described in the Nauru files.

“I have seen physical assaults, death, sexual abuse and torture. I have seen the deliberate denial of medical care, even for serious and potentially life-threatening conditions. If you saw what was happening here, you would have no doubt it is a system of punishment and deliberate cruelty,” he said.

Bouchani said he believed the system was against the values of Australian people.

“Once you understand what is happening here and in Nauru I know you cannot accept it. So I am asking you to do everything you can to help us, and end this cruelty. After all I’ve seen these last three years I believe the only way we will get freedom is when enough Australian people support us.”

The Sydney rally began at the city’s town hall, and marched past the Papua New Guinea consulate office on route to Circular Quay.

Nick Reimer, a spokesman for the RAC in Sydney, said between 3,000 and 5,000 people attended in what he believed was one of the biggest refugee rights demonstrations in Sydney for some time.

He said there was a variety of speakers, including union leaders, Father Rod Bower of the Gosford Anglican church, and an Afghan speaker, Habiba “who spoke about the omnipresence of danger and insecurity and death that people are fleeing from, and saying the only thing people who are fleeing to Australia want is freedom.”

In London protesters staged a live reading of all the incident reports contained in the Nauru files outside Australia House.

“The duration, monotony and repetition entailed in the reading of each file echoes the normalisation of the violence and tedium endured by refugees in indefinite detention,” said Sarah Keenan, a co-organiser of the event held by the International Alliance Against Mandatory Detention.

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The Australian and Papua New Guinean governments have confirmed the Manus Island facility will close, after the PNG supreme court ruled it illegal and unconstitutional in August, but there are no details on how it will happen or on the fate of the 854 men detained.

The Australian immigration minister, Peter Dutton, maintained that no asylum seekers or refugees would be brought to Australia.